There are several possible reasons for this…all speculation, of course, as there is nothing mentioned explicitly in the text as to why she did not go with him.

We would just have to make assumptions based on the knowledge of the epic, knowing the characters of Lakshman and Urmila and some basic common sense.

1 – When the decision was made NOT to take Urmila along, Lakshman wanted her to stay behind to look after Queen Kaushalya, whom Lord Ram feared would be neglected once Bharat became King.

2 – The 14-year sleep boon which was unknown to both of them at that point of time, but was put into practice during their period of separation. (I haven’t read this in the Valmiki Ramayana. Maybe it was a part of some regional version. As far as I understood, she was quite awake and looked after the affairs of the state, helping Shatrughan [in his role as the King’s deputy] as the presence in the palace, as Bharat was living in a self-imposed exile away from the Palace)

3 – If Urmila was with him, Lakshman would not have been able to look after his brother and sister-in-law with the same amount of dedication. His attention would have been divided. In her absence, Lakshman was more focused.

4 – Urmila was a lot more sensible and mature, and knew that if she accompanied him, she would only be a hindrance in the execution of his duties. She in fact extends her complete support to his purpose and tells him to perform his duties as their protector to the best of his abilities.

5 – Their love for each other was strong enough for both of them to not need each other’s physical presence with each other all the time. Urmila and Lakshman’s love for each other was, quite arguably, the strongest bonds of all the four couples.

6 – Destiny. If Urmila had accompanied Lakshman, she would have been there when Shurpanakha paid a visit and also with Sita in the hut when Raavan comes to abduct her. Things would have been very different then, and the purpose of Lord Ram’s birth would not have been fulfilled the way it was meant to be fulfilled.